Photos Library Borked

After turning on iCloud Photo Library, my carefully curated photo albums disappeared from my iOS (10.0.2) devices. Instead of "San Diego 2008" and "Grand Canyon," the only albums showing on my iPhone 7 and iPad Air 2 are the following:

All Photos

People (this is blank)

Places

Videos

Selfies

Screenshots

Recently Deleted

On my iMac (Sierra), the order my albums were in in the sidebar was shuffled.

Back to iOS 10, where all my custom stuff... Gone. Under "Photos" at the bottom, less than half my pictures are there 2,200 out of 5,400. And many of those appear as cloud blanks. The cloud blanks also dominate my OS X Photos app library. Before turning on iCloud Photo Library, all 5,400 of my pics were on my local Mac. This is a disaster!

Just completely signed out of iCloud on the Mac, rebooted, then signed back in. When I launched Photos, the cloud blanks turned to exclamation blanks. This is insane!

If I log into iCloud in Safari, all my pictures are there. The album order is all scrambled (but more easily fixable), but there's no apparent data loss. Only in the Photos OS X Sierra app and on iOS is stuff actually missing. There's got to be a way to reset the Photos app and make it redownload everything from iCloud.

I logged out of iCloud on all my mobile devices, then signed back in. All the albums now show, but there are pictures missing from most of them. An album will show 68 pictures in the macOS Photos app (and on the iCloud website), but only 17 of them show on my phone and iPad.